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A nonlinear galerkin method: The two-level fourier-collocation case

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Abstract

In this article we study the implementation of the Nonlinear Galerkin method as a multiresolution method when a two-level Fourier-collocation discretization is used. The set of collocation points with an even number of points is considered as the fine grid and decomposed into two coarse grids containing half as many points. Using these two grids we decompose the unknown into the sum of a large scale component containing only low frequency modes and based on one of the coarse grids and a small scale component containing only high frequency modes and based on the other coarse grid. This produces interesting connections between the physical space and the Fourier space representations of the function. A nonlinear Galerkin scheme is then applied to the Burgers equation; finally, implementation issues are discussed showing the advantages of the method.

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References

  • Dettori, L., Gottlieb, D., and Temam, E. Nonlinear Galerkin method: the two-level Chebyshev-collocation case (in preparation).

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, Rhode Island

    Lucia Dettori

  2. Laboratoire d'Analyse Numérique, Université Paris-Sud, Bât. 425, 91405, Orsay, France

    Lucia Dettori

  3. Division of Applied Mathematics, Brown University, 02912, Providence, Rhode Island

    David Gottlieb

  4. Laboratoire d'Analyse Numérique, Université Paris-Sud, Bât. 425, 91405, Orsay, France

    Roger Temam

  5. The Institute for Scientific Computing and Applied Mathematics, Indiana University, 618 East Third Street, 47405, Bloomington, Indiana

    Roger Temam

Authors
  1. Lucia Dettori
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  2. David Gottlieb
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  3. Roger Temam
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Dettori, L., Gottlieb, D. & Temam, R. A nonlinear galerkin method: The two-level fourier-collocation case. J Sci Comput 10, 371–389 (1995). https://doi.org/10.1007/BF02088956

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  • DOI: https://doi.org/10.1007/BF02088956

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